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Date: Fri, 3 Mar 2000 20:19:13 EST
From: pycyn@aol.com
Subject: [lojban] Final clubs.
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From: pycyn@aol.com

This is the sort of thing that usually works for these types of critters.  
sorry it is not in Lojban, it is hard enough in English.
1.  Call a set, s,  of clubs preclusive it being a member of any one of the 
clubs in s precludes being a member of any other club in s.
2.  Call a set, m, of clubs maximally preclusive if it is preclusive and 
every proper superset of it is not preclusive (i.e., adding any other club to 
the set destroys its preclusivity - someone could belong to the new club as 
well as to some club in m set).
Note, the empty set and all singletons are preclusive and some larrger sets 
may be.  But this is not yet necessarily sets of final clubs.  Each maximally 
preclusive set is final with repect to itself and some subset of the clubs, 
but not yet necessarily for the whole set of clubs.  However, 
3) the intersection of the set of all maximally preclusive sets (i.e., the 
set of clubs that are in every one of these max prec sets) is the set of 
final clubs for the whole set of clubs.  It is, of course, maximally 
preclusive and final over the whole set.  
So, the final clubs are those which are in all maximally preclusive sets of 
clubs.
I think.
pc
 

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